Download 101215 Scientific Notation v2

Scientific
Notation
Copyright © Science Stuff
Copyright © Science Stuff
Scientific Notation is used to express very large and
very small numbers so that problem solving will be
easier.
Examples:
The mass of one gold atom is
.000 000 000 000 000 000 000 327 grams.
One gram of hydrogen contains
602 000 000 000 000 000 000 000 hydrogen atoms.
Scientists can work with very large
and very small numbers more easily
if the numbers are written in
scientific notation.
How to Use Scientific
Notation
•In scientific notation, a number is
written as the product of two
numbers…..
…..A coefficient and
10 raised to a
power.
The number 4,500 is written in scientific
notation as ________________.
4.5 x 103
The coefficient is _______.
4.5
The coefficient must be a number
greater than or equal to 1
and smaller than 10.
The power of 10 or exponent in this
example is _____.
3
The exponent indicates how many times the
coefficient must be multiplied by 10 to equal
the original number of 4,500.
Rules to Remember!
If a number is greater than
10, the exponent will be
__________
positive and is equal to
the number of places the
decimal must be moved to
the right
_____ to write the
number in scientific
notation.
Rules to Remember!
If a number is less than 1, the
exponent will be
___________
negative and is equal to
the number of places the
decimal must be moved to
the _______
left to write the
number in scientific
notation.
A number will have an
exponent of zero if:
….the number is equal
to or greater than 1,
but less than 10.
1. Move the decimal to the right of the
first non-zero number.
2. Count how many places the decimal
had to be moved.
3. If the decimal had to be moved to the right,
the exponent is positive
4. If the decimal had to be moved to the left,
the exponent is negative.
To emphasize again: The exponent counts how many places you
move the decimal to the left or right.
Practice Problems
Express the following in scientific notation.
PROBLEMS:
1)
2)
3)
4)
5)
6)
0.00012
1000
0.01
12
0.987
596
ANSWERS
1)
2)
3)
4)
5)
6)
1.2 x 10-4
1 x 103
1 x 10-2
1.2 x 101
9.87 x 10-1
5.96 x 102
Practice Problems
Express the following in scientific notation.
PROBLEMS:
ANSWERS
-7
7.7.0
x
10
7) 0.000 000 7
6
8.
1.0
x
10
8) 1,000,000
-3
9.
1.26
x
10
9) 0.001257
10) 987,653,000,000 10. 9.88 x 1011
11) 8
11. 8 x 100
EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
1)
2)
3)
4)
5)
6)
7)
4.9 X 102
3.75 X 10-2
5.95 X 10-4
9.46 X 103
3.87 X 101
7.10 X 100
8.2 X 10-5
ANSWERS
1)490
2).0375
3).000595
4)9460
5)38.7
6)7.10
7).000082
Using Scientific
Notation in
Multiplication,
Division, Addition
and Subtraction
Scientists must be able
to use very large and
very small numbers in
mathematical
calculations. As a
student in this class,
you will have to be
able to multiply, divide,
add and subtract
numbers that are
written in scientific
notation. Here are the
rules.
***VERY IMPORTANT***
When computing with Scientific Notation, sometimes
you have to change the exponent. To do so, count how
many times you need to move the decimal.
 If you move the decimal forward, ADD that number
to the exponents.
 If you move the decimal backward, SUBTRACT
that number to the exponents
Rule for Multiplication
(on graphic organizer)
When multiplying numbers written in scientific
notation…..
Step 1: Multiply the decimal numbers
Step 2: Add the exponents (follow Exponent
Rule)
Step 3: Make sure you have one digit (non
zero) in front of the decimal
Example
(write all steps on Graphic organizer next to the written steps)
Evaluate (7.2 x 103 ) (1.6 x 104 ). Express in Scientific Notation.
STEP 1: Multiply decimal #s 
STEP 2: Add the exponents 
STEP 3: Put all together…
WAIT! Is that in Scientific Notation!!??!!??
STEP 4: Move decimal forward 1.. Add 1 to exponent
Guided Practice
(turn paper over or pg 220 )
(8.4 x 102 ) ( 2.5 x 106 )
STEP 1: Multiply decimal # 
STEP 2: Add the exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4:
Guided Practice
(turn paper over or pg 220 )
2
6
(2.63 x 10 )(2.5 𝑥 10 )
STEP 1: Multiply decimal # 
STEP 2: Add the exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4:
Rule for Division
(on graphic organizer)
When dividing numbers written in
scientific notation…
Step 1: Divide the decimal numbers
Step 2: Subtract exponents (follow
Exponent rules)
Step 3: Make sure you have one digit (non
zero) in front of the decimal
Example
(write all steps on Graphic organizer next to the written steps)
8.37 𝑥 108
Evaluate
. Express in Scientific Notation.
3
2.7 𝑥 10
STEP 1: Divide the decimal #s 
STEP 2: Subtract exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation???????
Yes. 3.1 is in between #s 1 and 10
Guided Practice
(turn paper over or pg 222 )
1.2 𝑥 107
2.4 𝑥 103
STEP 1: Divide the decimal #s 
STEP 2: Subtract exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
Guided Practice
(turn paper over )
4.64 𝑥 10−4
2.9 𝑥 10−6
STEP 1: Divide the decimal #s 
STEP 2: Subtract exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4:
Classwork: Complete
worksheet. Will check for
accuracy
HW pg 223 EVEN #s
Rule for Addition and Subtraction
(on Graphic Organizer)
To add or subtract numbers written in scientific
notation, you must….express them with the same
power of ten.
Step 1: Make sure that both exponents are the SAME! ** you
might have to move a decimal forward or backward to have
same exponent #s
Step 2: Add decimal #’s together
Step 3: Make sure it is in SCIENTIFIC NOTATION!
Example: Graphic
Organizer
Evaluate each expression. Express in Scientific Notation.
(6.89 x 104 ) + (9.24 x 105 )
Step 1: Exponents MUST be the same. Let’s make
9.24 x 105 as 92.4 x 104
Step 2: Add decimal #s
6.89 + 92.4 = 99.29
Step 3: Put it all together! 99.29 x 104
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
9.929 x 105
Example: Graphic
Organizer
Evaluate each expression. Express in Scientific Notation.
(1.03 x 109 ) - (4.7 x 107 )
Step 1: Exponents MUST be the same.
Step 2: Add decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice: Adding
(worksheet)
Evaluate each expression. Express in Scientific Notation.
(8.41 x 103 ) + (9.71 x 104 )
Step 1: Exponents MUST be the same.
Step 2: Add decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice: Adding
(worksheet)
Evaluate each expression. Express in Scientific Notation.
593,000+ (7.89 x 106 )
Step 1: Exponents MUST be the same.
Step 2: Add decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice:
Subtracting (worksheet)
Evaluate each expression. Express in Scientific Notation.
(1.263 x 109 ) + (1.525 x 107 )
Step 1: Exponents MUST be the same.
Step 2: Add decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice:
Subtracting (worksheet)
Evaluate each expression. Express in Scientific Notation.
11,610,000 - (7.83 x 108 )
Step 1: Exponents MUST be the same.
Step 2: Subtract decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Independent Work
MULTIPLY THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN
SCIENTIFIC NOTATION.
Problems:
1. (6 x 105) (1 x 102)
2. (4 x 106) (2 x 10-5)
3. (3.4 x 106) (1.8 x 103)
4. (8.1 x 10-7) (3.6 x 102)
5. (4.9 x 104) (6 x 10-3)
6. (5 x 10-5) (2 x 10-6)
7. (0.000 000 015) *
(101,654,000,000)
8. (10,456,300,950) *
(9,754,321)
1.
2.
3.
4.
5.
6.
7.
8.
Answers:
x 107
6
8 x 101
6.12 x 109
2.92 x 10-4
2.94 x 102
1 x 10-10
1.53 x 103
1.02 x 1017
DIVIDE THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN
SCIENTIFIC NOTATION.
Problems:
1. (6 x 105)  (2 x 104)
2. (8 x 103)  (2 x 10-5)
3.(7.4 x 104)  (1.8 x 103)
4.(8.19 x 10-4)  (1.6 x
102)
5.(4.3 x 103)  (6.1 x 10-3)
6. (8 x 10-5)  (2 x 10-6)
7. (0.000 009 023) 
(101,351,000)
8. (12,701,300,950) 
(4,754,321)
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
3 x 101
4 x 108
4.11 x 101
5.12 x 10-6
7.05 x 105
4 x 101
8.9 x 10-14
2.67 x 103
ADD OR SUBTRACT EACH OF THE FOLLOWING NUMBERS. GIVE
YOUR ANSWER IN SCIENTIFIC NOTATION.
Problems:
1. (6 x 104) + (3 x 104)
2. (6 x 10-5) - (3 x 10-5)
3. (1.4 x 105) + (1.4 x 103)
4. (8 x 104) - (1.6 x 102)
5. (4.9 x 105) + (6.1 x 10-3)
6. (8 x 10-5) - (5 x 10-6)
7. (0.079 323) +
(0.196,351,000)
8. (12,701,555,950) (40,754,321)
Answers:
1. 9 x 10 4
2. 3 x 10 -5
3. 1.41 x 10 5
4. 7.98 x 10 4
5. 4.9 x 10 5
6. 7.5 x 10 -5
7. 2.76 x 10 -1
8. 1.27 x 10 10
Created by Amy Brown – Science
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(aka Science Stuff)
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